NONLINEAR BOUNDARY-VALUE PROBLEMS FOR THE LYAPUNOV EQUATION IN THE SPACE [L.sub.P]

NONLINEAR BOUNDARY-VALUE PROBLEMS FOR THE LYAPUNOV EQUATION IN THE SPACE [L.sub.P]

We study boundary-value problems for a Lyapunov-type equation in the space [L.sub.p](I,[??](H)). Necessary and sufficient conditions for the solvability of the corresponding boundary-value problem are established both in linear and nonlinear cases. The solutions of the linear boundary-value problem...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-04, Vol.246 (3), p.394
Hauptverfasser: Panasenko, E.V, Pokutnyi, O.O
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Sprache:eng
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Differential equations
Parathyroid hormone
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Pokutnyi, O.O
description We study boundary-value problems for a Lyapunov-type equation in the space [L.sub.p](I,[??](H)). Necessary and sufficient conditions for the solvability of the corresponding boundary-value problem are established both in linear and nonlinear cases. The solutions of the linear boundary-value problem are constructed by using the generalized Green operator. It is proposed to find the approximate solutions of the nonlinear equation by using iterative Newton--Kantorovich-type algorithms.
doi_str_mv 10.1007/s10958-020-04747-8
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subjects Differential equations
Parathyroid hormone
title NONLINEAR BOUNDARY-VALUE PROBLEMS FOR THE LYAPUNOV EQUATION IN THE SPACE [L.sub.P]
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